A challenge of colour codes is that they are not naively fault-tolerant when using standard parity check circuits in which a single ancilla is used for a stabiliser measurement. Whereas fault-tolerant stabiliser readout with single ancilla qubits is possible in surface codes, other codes, including colour codes, require more sophisticated ancilla constructions. That is, for standard parity check circuits, some weight-one faults spread to weight-two faults that lead to a logical error for the 7-qubit colour code, as can be seen in the example in Fig. REF .
To overcome this problem, various schemes have been developed to make the stabiliser readout fault tolerant [1]}, [2]}, [3]}, [4]}. However, these schemes require a substantial resource overhead, as they are based on the use of multiple qubit ancilla states which need to be prepared and verified, typically in multi-partite entangled states [1]}, [2]}.
